Effect of Hysteresis on Interface Waves in Contact Surfaces

  • Kim, Noh-Yu (Department of Mechatronic Engineering, Korea University of Technology) ;
  • Yang, Seung-Yong (Department of Mechanical Engineering, Korea University of Technology and Education)
  • Received : 2010.11.19
  • Accepted : 2010.12.10
  • Published : 2010.12.30


This paper describes a theoretical model and acoustic analysis of hysteresis of contacting surfaces subject to compression pressure. Contacting surfaces known to be nonlinear and hysteretic is considered as a simple spring that has a complex stiffness connecting discontinuous displacements between two solid contact boundaries. Mathematical formulation for 1-D interfacial wave propagation between two contacting solids is developed using the complex spring model to derive the dispersion relation between the interface wave speed and the complex interfacial stiffness. Existence of the interface wave propagating along the hysteretic interface is studied in theory and discussed by investigating the solution to the dispersion equation. Unlike the linear interface without hysteresis, there can exist only one distinct mode of interface waves for the hysteretic interface, which is anti-symmetric motion. The anti-symmetric mode of interface wave propagates with the velocity faster than the Rayleigh surface wave but less than the shear wave depending on the interfacial stiffness. If the contacting surfaces are compressed so much that the linear interfacial stiffness is very high, the hysteretic stiffness does not affect the interface wave velocity. However, it has an effect on the speed of interface wave for a loosely contact surfaces with a relatively low linear stiffness. It is also found that the phase velocity of anti-symmetric wave mode converges to the shear wave velocity in despite of the linear stiffness value if the hysteretic stiffness approaches 0.5.


  1. Biwa, S., Hiraiwa, S. and Matsumoto, E. (2006) Experimental and Theoretical Study of Harmonic Generation at Contacting Interface, Ultrasonics, Vol. 44, pp. 1319-1322 https://doi.org/10.1016/j.ultras.2006.05.010
  2. Biwa, S., Hiraiwa, S. and Matsumoto, E. (2007) Stiffness Evaluation of Contacting Surfaces by Bulk and Interface Waves, Ultrasonics, Vol. 47, pp. 123-129 https://doi.org/10.1016/j.ultras.2007.08.005
  3. Kim, J. Y., Baltazar, A. and Rokhlin, S. I. (2004), Ultrasonic Assessment of Rough Surface Contact between Solids from Elasto-Plastic Loading-Unloading Hysteresis Cycle, Journal of the Mechanics and Physics of Solids, Vol. 52, pp. 1911-1934 https://doi.org/10.1016/j.jmps.2004.01.006
  4. Kim, N and Tang, S (2007) Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface, Journal of the Korean Society for Nondestructive Testing, Vol. 27, No. 6, pp. 582-590
  5. Meirovitch, L. (1967) Analytical Methods in Vibrations, MaCmillan Company, New York, USA, pp. 403-404
  6. Pecorari, C. and Rokhlin, S. I. (2007) Elasto-Plastic Micromechanical Model for Determination of Dynamic Stiffness and Real Contact Area from Ultrasonic Measurements, Wear, Vol. 262, pp. 905-913. https://doi.org/10.1016/j.wear.2006.08.018
  7. Solodov, I. Y. (1998) Ultrasonics of Non-Linear Contacts: Propagation, Reflection, and NDE Applications, Ultrasonics, Vol. 36, pp. 383-390 https://doi.org/10.1016/S0041-624X(97)00041-3